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Abstract

There is currently great interest in determining physical parameters, e.g. fluorescence lifetime, of individual molecules that inform on environmental conditions, whilst avoiding the artefacts of ensemble averaging. Protein interactions, molecular dynamics and sub-species can all be studied. In a burst integrated fluorescence lifetime (BIFL) experiment, identification of fluorescent bursts from single molecules above background detection is a problem. This paper presents a Bayesian method for burst identification based on model selection and demonstrates the detection of bursts consisting of 10% signal amplitude. The method also estimates the fluorescence lifetime (and its error) from the burst data.

Figures (3)

A simplified schematic illustrating the mathematical process of forming the posterior probability density function (PDF, blue lines) versus lifetime, from which the most likely lifetime and an associated error interval can be calculated. Starting from the prior probability density function, successive photon arrival times (red bars, shown at the appropriate microtime) contribute some evidence under this Bayesian framework, as calculated by the function F (see text). As more photons are measured the posterior PDF may become a single well-defined peak indicating the most likely lifetime value, w1.

Bayesian burst detection from simulated data. Signal fluorescence lifetime is set to 2 ns in all cases. (a) Bursts where the signal proportion of 1/3 (bg: 2 x 104 s−1 sig: 1 x 104 s−1) are easily detected (and would equally be by simple thresholding of the macrotime trace). (b) Bursts with a signal proportion of 1/10 (bg: 2 x 104 s−1 sig: 2 x 103 s−1) cannot be detected from the macrotime trace alone. The Bayesian technique detects these bursts as shown by the resulting probability of a signal, P(signal) = P(Hsig|D) (red line). (c) The microtime trace with 1/3 signal, extracted from the photon train near 0.8 seconds (see dotted line labelled ‘c’ in (a)). (d and e) Microtime traces representing 1/10 signal and pure background noise (see dotted lines in (b)). Microtime traces were formed from data re-binned into 100 bins for plotting clarity. Where bursts were detected, lifetime fitting was performed by the full continuous Bayes algorithm on the re-binned data. The fitted curves are shown (solid line) and on the right hand side (f and g) are plots of the 2D PDF around the most likely value, where white indicates high values, decreasing through a spectrum to black which indicate low values. (h) The percentage of true detected bursts (blue line) and false positive detections (red line) as a function of signal proportion. (‘counts’ = number of photon counts in trace, ‘lifetime’ = determined lifetime).

Bayesian burst detection from experimental data of a dilute solution of quantum dots. (a) Macrotime intensity trace and corresponding signal probability. The obvious high-intensity burst is detected along with several low intensity bursts that are not apparent through analysis of the macrotime trace alone. (b, c and d) Microtime traces extracted from the photon train at the positions indicated by the dotted lines in (a). Lifetime fitting was performed on the microtime data and the fitted curve is shown (solid line, re-binned into 32 bins for clarity) and inset is a plot of the PDF around the most likely value. Data in graph (c) was rejected as background since P(signal) is below 0.5. Lifetimes of 6.20 ns and 4.88 ns were extracted by a full, continuous, Bayesian analysis of the high- and low-intensity bursts, respectively.